Text only print
Full screen print
Tokyo Probability Seminar
Seminar information archive ～10/16｜Next seminar｜Future seminars 10/17～
| Date, time & place | Monday 16:00 - 17:30 122Room #122 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima (Keio Univ.), Masato Hoshino (Science Tokyo), Masahisa Ebina (Science Tokyo) |
Next seminar
2026/10/19
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Kohki Sakamoto (The University of Tokyo)
Singularity of harmonic measure on Poisson-Voronoi tessellations in hyperbolic spaces
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Kohki Sakamoto (The University of Tokyo)
Singularity of harmonic measure on Poisson-Voronoi tessellations in hyperbolic spaces
[ Abstract ]
Poisson-Voronoi tessellations provide natural examples of invariant random tilings of homogeneous spaces. Benjamini, Paquette, and Pfeffer proved that the nearest-neighbor random walk on the Poisson-Voronoi tessellation of the hyperbolic plane has positive drift and hence converges to the boundary circle. They further conjectured that its hitting measure on the boundary is singular with respect to Lebesgue measure. I will explain how this follows from an ergodic-theoretic argument based on rerooting relations, and briefly discuss the higher-dimensional case as well.
Poisson-Voronoi tessellations provide natural examples of invariant random tilings of homogeneous spaces. Benjamini, Paquette, and Pfeffer proved that the nearest-neighbor random walk on the Poisson-Voronoi tessellation of the hyperbolic plane has positive drift and hence converges to the boundary circle. They further conjectured that its hitting measure on the boundary is singular with respect to Lebesgue measure. I will explain how this follows from an ergodic-theoretic argument based on rerooting relations, and briefly discuss the higher-dimensional case as well.
